The mean, median and mode

After you have collected some data, you usually want a way to describe or summarize it with just a few numbers. Most importantly, you will want a single number that captures the central tendency of the data. There are several ways to measure the central tendency, and the best choice depends on the nature of the data at hand. The following are the most commonly used:

Arithmetic mean

The arithmetic mean, also known as the average or simply the mean, is the sum of all of the numbers in the data set divided by the size of the data set.

Median

The median is the value that is in the middle when the numbers in a data set are sorted in increasing order. An advantage of the median over the mean is that it is less sensitive to extreme values in the data set (which may be outliers or measurement errors).

Mode

The mode is that value that occurs most often in the data.

Example

Assume you would like to measure the level of social anxiety among a sample of 21 people. Each person fills out the Fear of Negative Evaluation (FNE) scale, which gives them a score from 0 to 30. Let's assume you get the following results:

10, 12, 16, 16, 25, 5, 13, 15, 20, 20, 18, 16, 15, 10, 16, 20, 9, 14, 18, 13, 11

Arithmetic mean

Adding up all the numbers and dividing by 21 gives the result 14.86.

Median

If we arrange the numbers from smallest to largest we get:

5, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15, 16, 16, 16, 16, 18, 18, 20, 20, 20, 25

To find the median we note that the value in the middle (position 11) is 15.

Mode

We can also find the mode by looking at the sorted results. Four people had the score 16, which is more than any other value. Therefore, the mode is 16.